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I think all are possible: Reason being, to construct a triangle all that we need is a set of 3 distinct points and in this case we can bring 3 points as close as possible and also make it lie the circle (your imagination should work here).
i think the answer should 1, 2 and 3 are all possible..
hi fresinha, the radius of the circle is 1 units That means that the distance between the center of the circle and the vertices of the triangle is 1 i.e the radius .so when the internal distances are 1 how can the perimeter be <0
Which of the following can be a perimeter of a triangle inscribed in a circle of radius 1?
I only III only II and III only I, II, and III not I, II, or III
As we can see, a triangle with 3 sides: a, b, c which is inscribed in a circle with the radius is 1. We assume a is the biggest side of the triangle. We have the perimeter = a + b + c > a + a = 2a Because the triangle is inscribled in a circle so a is always smaller than or equal to the diameter = 2. So, we have the perimeter > 2a >= 4. So E is the correct answer.
The point of giving the radius is just confusing the test takers. It doesn't matter at all. We have to place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle. Do you agree? _________________
The point of giving the radius is just confusing the test takers. It doesn't matter at all. We have to place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle. Do you agree?
boy this question did my head in today! nice tricky question and a great explanation. Can we update the explanation in the test with this one please. The OE in the test leaves a lot to be desired.
Even if it is not given the inscribed triangle is equilateral triangle , let's assume that the traingle is equilateral .
For an equilateral triangle inscribed in a circle side s = sqroot(3)*r ; with r =1 , side s = root(3) , so perimeter is 3*root(3) . Which is way off all the choices given in the question
intutively I think other triangle inscribed in the circle will have perimeter greater than equilateral triangle , but I don't have a good reasoning , I might be wrong . If some quant expert shed some light on this , would be great !